The invention relates to a method for improving the definition of a digitized image whose image elements are stored light-intensity values that are organized in rows and columns as an output matrix Axy, with a respective matrix section Aij of 2nxc3x972m elements being expanded, through reflection at two of its adjacent edges, and the corner formed by these edges, to 2n+1xc3x972m+1 elements, then subjected to a Fourier transformation. The resulting transformed matrix, Bij, 1xe2x89xa6ixe2x89xa62n+1, 1xe2x89xa6jxe2x89xa62m+1, is converted through elementary multiplication with an image-aberration correction matrix Cij (all elements being real) into a corrected, transformed matrix Bxe2x80x2ij, and is transformed back into an intensity matrix Axe2x80x2ij, from which a core section is set into the center of a corrected intensity matrix Axe2x80x2xy, corresponding to the position of the matrix section Aij; then, one matrix section is processed after another in this way, staggered by one edge length of the core section, until a complete, corrected intensity matrix Axe2x80x2xy is obtained.
A method of this type is known from Ohm, J. -R.:Digitale Bildcodierung [Digital Image Encoding], Springer 1995, pp. 33/34, 56/57. This processing of local matrix regions with the inclusion of a reflected environment reduces the occurrence of edge disturbances in the image regions, and effects an accelerated processing of the entire matrix.
Moreover, Wahl, F. M. discloses an image processing in the local frequency range only for locally-invariant systems in Digitale Bildsignalverarbeitung [Image Signal Processing], Springer 1984. For image-recording systems possessing locally-varying properties, such as a resolution capability that changes from location to location, local-frequency distortions of image signals are partially compensated with locally-varying filters. In these systems, the local-frequency transmission behavior is a function of the local coordinates. For each image point, therefore, a set of suitable filter coefficients would have to be determined, but to reduce costs, the locally-varying filter only comprises a few filters arranged by image regions.
It is also known to change the stored light-intensity values of the individual pixels of an image in its contrast by adding a background-brightness value and/or through the spreading or normalization of the value range; these modifications can also be implemented separately for different color-image components that are stored as separate value fields. This improves the visual appearance of an image produced with image data that have been modified in this manner; it is not possible, however, to eliminate blurring of the output image with this procedure.
It is the object of the invention to provide an effective method of improving the definition of images with regard to image aberrations of a lens.
The solution lies in suitably determining the image-aberration correction matrix according to a respective location-dependent aberration-correction matrices from an MTF, that is, modulation-transfer function correction function to match given MTF values of a lens used to image the digitized image, and selecting these local aberration-correction matrices as a subset of the image-aberration correction matrix, corresponding to the position of the associated matrix section, relative to the position of a center point of an image circle, and the distance and the tangential and radial angles of the edges of the matrix section from this central point.
The dependent claims disclose advantageous embodiments.
If the lens and the scale of the image are known, the tangential and radial frequency spread according to the position in the image circle can be taken from the MTF modulation tables of the lens. The correction factor for the individual frequencies results as the reciprocal value of the so-called modulation degree in the respective image circle, namely in the radial and tangential directions to the circle.
If the lens data or the recording data are unknown, according to an embodiment of the method, individual marked image sections are selected, and their processing parameters are varied until a desired optimum definition is achieved. The entire correction matrix can then be derived through fitting from a parametrized correction function. A tried-and-true function is described below.
The novel method operates in the frequency space, with the frequency information for processing the local values being drawn from the surroundings of a small image section. To assure a processing of the individual image sections that is untainted by marginal conditions, the segment""s matrix values are reflected three times in different directions, yielding a completely-symmetrical matrix that is twice as large. The spectrum of a matrix of this type is free from marginal interferences.
The entire digital image is gradually processed in this manner, and the matrix values of the individual sections are reworked by an elementary multiplication with a local section of a correction matrix. A subset of the individual result matrix, as the core section, is then transformed back into a result matrix in the intensity range until the matrix is completely formed from these subsets. The core section used after the inverse transformation is preferably a subset corresponding to (2nxe2x88x92k1)xc3x97(2mxe2x88x92k2); 0 less than k1, k2 less than 22n, 2m elements of the original matrix section Aij, and, accordingly, its edge lengths are 2nxe2x88x92k1 or 2mxe2x88x92k2, by which core sections are staggered in their arrangement. The known modifications of the elements can therefore be implemented in the amplitude space as desired.
The actual definition of the contours appears in the frequency space through processing, namely through the increase in the high frequency components to the extent that they decreased at the relevant location in the image.
In a further embodiment of the method, a correction function for the radial and tangential image components is derived from the MTF table of the lens. The associated correction function is then calculated from the radial and tangential correction-function values of the two correction functions through interpolation, with consideration of the respective position of the edge of the matrix subset relative to the image circle.
The processing time for an image is heavily dependent on the size of the selected matrix sections. On the other hand, the larger the section, the greater the attainable improvement in definition, although a considerable enlargement does not yield much improvement. In contrast, if the number of matrix elements is too low, the statistical noise is amplified, so raised xe2x80x9cseeds and saltxe2x80x9d appear on a matte surface: For example, the grain of a reproduced photo or the sieve structure of a reproduced print disadvantageously appears. An image section of 8xc3x978 or 16xc3x9716 elements, with a core of 4xc3x974 or 8xc3x978 sharpened elements ultimately being used, has proven advantageous in practice.
Because the image edge of the selected core regions, which are smaller than the sections, does not extend to the original image edge, the inverse-transformed image-element values remaining there after the core has been extracted can be used to fill the edge region. As an alternative, one or more rows of the original matrix elements can be reflected around the image edge prior to the transformation, which creates a slightly larger output matrix, so the core regions arranged together cover the entire original matrix size, and the reflected edge region is omitted and not filled.
In a modification of the method, in the case of a plurality of image-value matrices that are divided by color, they are separated and, provided that they are known, they are corrected with the correction function specified for the respective color. Moreover, the individual color-image matrices are advantageously converted into a matching format through a radial expansion or compression in the image circle; the different imaging scales of the lens are compensated for the individual colors. This process eliminates unattractive color fringes along the sharply-defined edges.
If the color aberrations are not known to the device, they can be determined through an analysis of color-intensity value courses for selected image sections, particularly those containing the edges that are tangential to the image circle, in that the relative displacements of the transitions of the edges that have been sharpened through processing are determined in the individual color-image matrices, and the degree of the expansion or compression to which the respective result matrix is then subjected is determined from the displacements in relation to their position in the image circle.
Thus, the method and its embodiments can be employed following digitizing to correct images that have been recorded with unknown lenses and with blurring, with respect to different types of imaging errors, especially relative to their definition and color aberrations.
A correction function that is suitable for the entire image can be determined through a sectional processing by means of a step-wise approximation, or from the MTF characteristic values of the lens and the imaging parameters, provided that they are known. Factors to be considered here are, for example, the location in the image circle, that is, the distance of the element in the image plane from the optical axis of the imaging lens, the direction radially or tangentially or at an angle to the image circle of the image elements or matrix elements, the opening ratio, the inclination of the image plane relative to the lens plane and, if applicable, the color.